Image Encryption Technology Based on Fractional Two-Dimensional Discrete Chaotic Map Accompanied With Menezes-Vanstone Elliptic Curve Cryptosystem

Liu, Zeyu; Xia, Tiecheng; Wang, Yiping

doi:10.1142/s0218348x2150064x

Cited by 9 publications

(5 citation statements)

References 31 publications

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“…The application of discrete fractional neural networks to encryption was presented in [27]. The elliptic curve cryptosystem and the 2D fractional-order discrete map are employed for the process of encryption in [28]. Wu et al presented the technique of encryption of images with chaotic fractional discrete time series in [29] and a novel technique was introduced in [30].…”

Section: Introductionmentioning

confidence: 99%

A Novel Fractional Sine Chaotic Map and Its Application to Image Encryption and Watermarking

2023

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This article addresses the telecommunications industry’s priority of ensuring information security during the transition to next-generation networks. It proposes an image encryption system that combines watermarking techniques and a discrete fractional sine chaotic map. The authors also incorporate the principles of blockchain to enhance the security of transmitted and received image data. The proposed system utilizes a newly developed sine chaotic map with a fractional difference operator, exhibiting long-term chaotic dynamics. The complexity of this map is demonstrated by comparing it with three other fractional chaotic maps from existing literature, using bifurcation diagrams and the largest Lyapunov exponent. The authors also show the map’s sensitivity to changes in initial conditions through time-series diagrams. To encrypt images, the authors suggest a method involving watermarking of two secret images and encryption based on blockchain technology. The cover image is watermarked with the two hidden images using discrete wavelet transformations. Then, the image pixels undergo diffusion using a chaotic matrix generated from the discrete fractional sine chaotic map. This encryption process aims to protect the image data and make it resistant to unauthorized access. To evaluate the algorithm, the authors perform statistical analysis and critical sensitivity analysis to examine its characteristics. They also analyse different attacks to assess the algorithm’s ability to resist such threats and maintain image quality after decryption. The results demonstrate that the proposed algorithm effectively defends against attacks and ensures image security.

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Section: Introductionmentioning

confidence: 99%

A Novel Fractional Sine Chaotic Map and Its Application to Image Encryption and Watermarking

2023

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“…A discrete chaotic map involving fractional calculus has complex dynamics. Furthermore, it is not only sensitive to a small disturbance in parameters and initial conditions, but also to the change in fractional orders [26]. Therefore, fractional-order discrete maps, with simple forms and rich dynamics, are more suitable for data encryption and secure communication [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Sinusoidal Discrete Map

Liu

Tang

Hong

2022

Entropy

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In this paper, a novel fractional-order discrete map with a sinusoidal function possessing typical nonlinear features, including chaos and bifurcations, is proposed. Firstly, the basic properties involving the stability of the equilibrium points and the symmetry of the map are studied by theoretical analysis. Secondly, the dynamics of the map in commensurate-order and incommensurate-order cases with initial conditions belonging to different basins of attraction is investigated by numerical simulations. The bifurcation types and influential parameters of the map are analyzed via nonlinear tools. Hopf, period-doubling, and symmetry-breaking bifurcations are observed when a parameter or an order is varied. Bifurcation diagrams and maximum Lyapunov exponent spectrums, with both a variation in a system parameter and an order or two orders, are shown in a three-dimensional space. A comparison of the bifurcations in fractional-order and integral-order cases shows that the variation in an order has no effect on the symmetry-breaking bifurcation point. Finally, the heterogeneous hybrid synchronization of the map is realized by designing suitable controllers. It is worth noting that the increase in a derivative order can promote the synchronization speed for the fractional-order discrete map.

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“…Based on these, many fractional-order maps are proposed and studied in detail, such as fractional sine map, standard map, Hénon map, and Ikeda map [8][9][10][11][12][13][14]. For the long-term memory characteristic of the operator, this kind of maps is a better fit for application in secure communications and encryption [15][16][17]. The main reasons are that fractional-order discrete maps are not only sensitive to the small disturbance of parameters and initial conditions but also to the variation of fractional orders, which are the unique advantages of fractional-order systems.…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Discrete Lorenz Map

Xie

2022

Advances in Mathematical Physics

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In this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate-order and incommensurate-order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic-doubling cascade are found by the numerical simulations. The parameter values of Hopf bifurcation points are determined when the order is taken as a different value. It can be concluded that the parameter decreases as the order increases. Chaos control and synchronization for the fractional-order discrete Lorenz map are studied through designing the suitable controllers. The effectiveness of the controllers is illustrated by numerical simulations.

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Image Encryption Technology Based on Fractional Two-Dimensional Discrete Chaotic Map Accompanied With Menezes-Vanstone Elliptic Curve Cryptosystem

Cited by 9 publications

References 31 publications

A Novel Fractional Sine Chaotic Map and Its Application to Image Encryption and Watermarking

A Novel Fractional Sine Chaotic Map and Its Application to Image Encryption and Watermarking

A Fractional-Order Sinusoidal Discrete Map

A Fractional-Order Discrete Lorenz Map

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